In the conventional dewatering presses which are disclosed in U.S. Pat. Nos. 4,615,801, 4,755,291, 4,844,799 and 4,976,853, a single screw press with a filtering cylinder installed thereon presses and moves the waste materials, so that the dewatering should be carried out through the filtering cylinder. Therefore, in accordance with the waste material discharge amounts of factories, the capacity of the screw press has to be different, and the screw press of the corresponding capacity has to be installed. Therefore, the manufacturing cost is increased, and, in the case where a plurality of screw presses are installed, a large amount of power is consumed. Further, the apparatus occupies much space, and the pressure adjusting valves which are installed on the respective screw presses have to be driven by separate motors. Further, the outer circumference of the filtering cylinder is washed with a pressure water, a pressure air or a high pressure steam, and therefore, the residue waste materials adhered on the outside of the cylinder cannot be effectively cleaned.